Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller?Segel system
Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller?Segel system
复制标题
局部空间热演化方程的极大正则性及其在Keller?Segel系统奇异极限问题中的应用
DOI：
10.1007/s00208-022-02469-7
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发表时间：
2022
影响因子：
1.4
通讯作者：
Suguro Takeshi
中科院分区：
文献类型：
--
作者：
Ogawa Takayoshi;Suguro Takeshi
我们考虑抛物线-抛物线型 (Patlak-) Keller-Segel 系统的柯西问题的奇异极限问题。在均匀局部勒贝格空间和奇异极限问题中考虑该问题，当松弛参数趋于无穷大时，Keller-Segel方程的解收敛于强均匀局部拓扑中的漂移扩散系统的解。为了证明，我们遵循 Kurokiba-Okawa [-] 的前一个结果，并在均匀局部 Lebesgue 和 Morrey 空间（非 UMD Banach 空间）上建立热方程的最大正则性，并将其应用于缩放关键局部空间中奇异极限问题的强收敛。
We consider the singular limit problem for the Cauchy problem of the (Patlak–) Keller–Segel system of parabolic-parabolic type. The problem is considered in the uniformly local Lebesgue spaces and the singular limit problem as the relaxation parametergoes to infinity, the solution to the Keller–Segel equation converges to a solution to the drift-diffusion system in the strong uniformly local topology. For the proof, we follow the former result due to Kurokiba–Ogawa [–] and we establish maximal regularity for the heat equation over the uniformly local Lebesgue and Morrey spaces which are non-UMD Banach spaces and apply it for the strong convergence of the singular limit problem in the scaling critical local spaces.